This is question of Permutation And Combination..In a Shooting competition, a man can score 5,4,3,2,1, or 0 points for each shot. Number of different ways in which he can score 30 in SEVEN shots.Answer= 420

This can be solved using an organized casework:

5555550 can be arranged in 7 ways.

5555532 can be arranged in 42 ways.

5555442 can be arranged in 105 ways.

5555433 can be arranged in 105 ways.

5554443 can be arranged in 140 ways.

5544444 can be arranged in 21 ways.

7+42+105+105+140+21=420 

Regards

Arun (askIITians forum expert)